8. Definite Integrals

Suppose the graph of a continuous function $f$ is shown below, and the area between the graph of $f$ and the $x$-axis from $x=0$ to $x=2$ is $3$ (above the $x$-axis), and from $x=2$ to $x=4$ is $2$ (below the $x$-axis). What is the value of the definite integral ${\int }_0^{4}f\left(x\right)dx$?

Let $g\left(x\right)={\int }_0^{x}f\left(t\right) dt$, where $f$ is the function whose graph is shown. Which of the following statements is true about $g^{\prime }\left(x\right)$?